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The Theory of Thermodynamic Systems with Internal Variables of State: Necessary and Sufficient Conditions for Compliance with the Second Law of Thermodynamics

  • GENERAL PROBLEMS OF TRANSFER THEORY
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Journal of Engineering Physics and Thermophysics Aims and scope

Based on the entropy-free thermodynamic approach, a generalized theory of thermodynamic systems with internal variables of state is being developed. For the case of nonlinear thermodynamic systems with internal variables of state and linear relaxation, the necessary and sufficient conditions have been proved for fulfillment of the second law of thermodynamics in entropy-free formulation which, according to the basic theorem of the theory, are also necessary and sufficient for the existence of a thermodynamic potential. Moreover, relations of correspondence between thermodynamic systems with memory and systems with internal variables of state have been established, as well as some useful relations in the spaces of states of both types of systems.

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References

  1. C. Truesdell, Rational Thermodynamics, Springer, Berlin (1976).

    MATH  Google Scholar 

  2. B. D. Coleman, Thermodynamics of materials with memory, Arch. Ration. Mech. Anal., 17, No. 1, 1–45 (1964).

    Article  MathSciNet  Google Scholar 

  3. W. A. Day, Thermodynamics of Simple Media with Memory [Russian translation], Mir, Moscow (1974).

    Google Scholar 

  4. B. D. Coleman and M. E. Gurtin, Thermodynamics with internal state variables, J. Chem. Phys., 47, No. 2, 597–613 (1967).

    Article  Google Scholar 

  5. V. L. Kolpashchikov and A. I. Shnip, Linear thermodynamic systems with memory. II. Necessary and sufficient conditions for applicability of the second law of thermodynamics, J. Eng. Phys. Thermophys., 68, No. 5, 584–594 (1995).

    Article  Google Scholar 

  6. A. I. Shnip, Theory of thermodynamic systems with memory, J. Eng. Phys. Thermophys., 75, No. 1, 26–40 (2002).

    Article  Google Scholar 

  7. C. Truesdell and W. Noll, The non-linear field theories of mechanics, in: S. Fliigge (Ed.), Handbuch der Physik, Springer, Berlin (1965), Vol. 111/3, pp. 1–602.

    Google Scholar 

  8. M. E. Gurtin and A. C. Pipkin, A theory of heat conduction with finite wave speeds, Arch. Ration. Mech. Anal., 31, 113−126 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  9. P. J. Chen and M. E. Gurtin, On second sound in materials with memory, Z. Angew. Math. Phys., 21, No. 3, 232−241 (1970).

    Article  MATH  Google Scholar 

  10. B. D. Coleman and E. N. Dill, On the thermodynamics of electromagnetic fields in materials with memory, Arch. Ration. Mech. Anal., 47, 132−162 (1971).

    Article  MathSciNet  Google Scholar 

  11. B. D. Coleman and D. R. Owen, A mathematical foundation for thermodynamics, Arch. Ration. Mech. Anal., 54, No. 1, 1−102 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Willems, Linear systems with quadratic supply rates, Arch. Ration. Mech. Anal., 45, 321−393 (1972).

  13. J. Willems, Realisation of systems with internal passivity and symmetry constraints, J. Franklin Inst., 301, No. 6, 605-621 (1978).

    Article  MATH  Google Scholar 

  14. V. T. Borukhov and A. I. Shnip, Subordinated systems and dissipative inequality for linear finite-dimensional passive systems, Syst. Sci., 25, No. 4, 15–24 (1999).

    MathSciNet  MATH  Google Scholar 

  15. V. T. Borukhov, A. I. Shnip, and D. M. Zelenyak, Storage functionals and Lyapunov functions for passive dynamical systems, Syst. Sci., 27, No. 2, 27–35 (2001).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., Minsk, 220072, Belarus

    A. I. Shnip

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  1. A. I. Shnip
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Correspondence to A. I. Shnip.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 1, pp. 5–21, January–February, 2018.

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Shnip, A.I. The Theory of Thermodynamic Systems with Internal Variables of State: Necessary and Sufficient Conditions for Compliance with the Second Law of Thermodynamics. J Eng Phys Thermophy 91, 1–15 (2018). https://doi.org/10.1007/s10891-018-1714-2

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  • DOI: https://doi.org/10.1007/s10891-018-1714-2

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